Yes, of course you are right - this only works in FBX.

But, even if you export to FBH
(I didn’t use it before because it didn’t work correctly. I haven’t tested it in version 4 yet) -
all the same, the objects will have one pivot point: the coordinate center MOI3d.

Ideally, it would be cool if you can implement the "binding" of individual pivots to objects (where necessary) and subsequent export to FBX.

As a matter of fact, I meant the principle itself. ))
Thanks for the answer and attention to my stupid questions.

This is how it looks in Blender:
Left cube - pivot in ulu cube, central cube - pivot to the center of the cube, the right cube is the pivot outside the cube.